Advanced numerical methods for multiphysics Magnetohydrodynamics

该项目的目标是开发创新的数值方法，能够在可再生能源和替代能源的背景下解决与能源有关的问题。该项目开发的数值技术将有助于设计能够储存大量可再生能源的网格规模的液态金属电池。这项研究还将有助于提高含有铁磁性颗粒的环保型植物油冷却的大功率电力变压器的性能。最后，通过促进理解液态金属中的磁流体动力不稳定性，该项目将有助于确定电磁泵的完整性和效率，这些泵将用于从下一代液态金属快中子增殖堆和托卡马克中提取能量。该项目将与一个欧洲团队合作完成；该项目将促进多样性、国际交流和多学科。该项目的教育部分将有助于提高美国STEM劳动力在计算磁流体力学方面的竞争力。该研究计划将被组织为四个领域：(1)开发新的有效的半隐式算法，以使用谱或极高阶方法来求解具有可变材料性质(密度、电导率、磁导率)的偏微分方程组；(2)铁磁流体的建模和新的数值技术的发展，以在液态金属和铁磁流体的背景下求解静磁方程；(3)开发考虑两个以上阶段的水平集技术，并开发新的高阶水平集技术以保证质量守恒和最大值原理；(4)将(1)-(2)-(3)中开发的数学模型和数值技术集成到大规模并行开放源代码中，以测试所提出的方法在实际应用(液态金属电池、高压变压器中铁磁油的热对流、液态金属发电机)中的应用。该项目将涉及首席研究员、一名博士后合作者、一名研究生和欧洲合作者。

The objective of this project is to develop innovative numerical methods capable of solving energy-related problems in the context of renewable and alternative energies. The numerical techniques developed in this project will help design grid-scale liquid metal batteries capable of storing large quantities of renewable energies. This research will also help improve the performance of large power electric transformers cooled by environment-friendly vegetable-based oils containing ferromagnetic particles. Finally, by facilitating the understanding of magneto-hydrodynamic instabilities in liquid metals, this project will help to ascertain the integrity and the efficiency of the electromagnetic pumps that will be used to extract energy from the next generation of Liquid-Metal Fast-Breeder Reactors and Tokamaks. This project will be done in collaboration with an European team; the project will foster diversity, international exchanges, and multidisciplinarity. The educational component of the project will contribute to increase the competitiveness of the STEM workforce in the US in computational magnetohydrodynamics.The research program will be organized into four areas: (1) Development of new efficient semi-implicit algorithms to solve partial differential equations with variable material properties (density, electric conductivity, magnetic permeability) using spectral or very high-order methods; (2) Modeling of ferromagnetic fluids and development of new numerical techniques to solve the magneto-static equations in the context of liquid metals and ferromagnetic fluids; (3) Development of level set techniques to account for more than two phases, and development of new high-order level set techniques to guarantee mass conservation and maximum principle; (4) Integration of the mathematical models and numerical techniques developed in (1)-(2)-(3) into a massively parallel open source code to test the proposed methods on realistic applications (liquid metal batteries, thermo-convection of ferromagnetic oil in high-voltage transformers, liquid metal dynamos). This project will involve the Principal Investigator, one post-doctoral collaborator, one graduate student, and European collaborators.